Assessment of ASSERT-PV for prediction of critical heat flux in CANDU bundles

Nuclear Engineering and Design 276 (2014) 216–227

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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes

Assessment of ASSERT-PV for prediction of critical heat flux in CANDU bundles Y.F. Rao ∗ , Z. Cheng, G.M. Waddington Atomic Energy of Canada Limited, Chalk River, ON, Canada K0J 1J0

h i g h l i g h t s • • • •

Assessment of the new Canadian subchannel code ASSERT-PV 3.2 for CHF prediction. CANDU 28-, 37- and 43-element bundle CHF experiments. Prediction improvement of ASSERT-PV 3.2 over previous code versions. Sensitivity study of the effect of CHF model options.

a r t i c l e

i n f o

Article history: Received 1 May 2014 Received in revised form 11 June 2014 Accepted 14 June 2014

a b s t r a c t Atomic Energy of Canada Limited (AECL) has developed the subchannel thermalhydraulics code ASSERTPV for the Canadian nuclear industry. The recently released ASSERT-PV 3.2 provides enhanced models for improved predictions of flow distribution, critical heat flux (CHF), and post-dryout (PDO) heat transfer in horizontal CANDU fuel channels. This paper presents results of an assessment of the new code version against five full-scale CANDU bundle experiments conducted in 1990s and in 2009 by Stern Laboratories (SL), using 28-, 37- and 43-element (CANFLEX) bundles. A total of 15 CHF test series with varying pressure-tube creep and/or bearing-pad height were analyzed. The SL experiments encompassed the bundle geometries and range of flow conditions for the intended ASSERT-PV applications for CANDU reactors. Code predictions of channel dryout power and axial and radial CHF locations were compared against measurements from the SL CHF tests to quantify the code prediction accuracy. The prediction statistics using the recommended model set of ASSERT-PV 3.2 were compared to those from previous code versions. Furthermore, the sensitivity studies evaluated the contribution of each CHF model change or enhancement to the improvement in CHF prediction. Overall, the assessment demonstrated significant improvement in prediction of channel dryout power and axial and radial CHF locations in horizontal fuel channels containing CANDU bundles. Crown Copyright © 2014 Published by Elsevier B.V. All rights reserved.

1. Introduction ASSERT-PV (advanced solution of subchannel equations in reactor thermalhydraulics, pressure–velocity solution procedure) (Carver et al., 1990; Carlucci et al., 2004; Rao and Hammouda, 2003) is a computer code developed at AECL mainly for thermalhydraulic analysis of CANDU reactor fuel bundles. The code is also capable of modeling other reactor fuel bundles, including PWR and BWR assemblies in vertical or horizontal channels. As well, the code can accommodate a range of fluids, including single-and two-phase heavy water, light water, various Freons, and an air–water mixture.

∗ Corresponding author. Tel.: +1 613 584 3311x46346. E-mail addresses: [email protected] (Y.F. Rao), [email protected] (Z. Cheng), [email protected] (G.M. Waddington). http://dx.doi.org/10.1016/j.nucengdes.2014.06.004 0029-5493/Crown Copyright © 2014 Published by Elsevier B.V. All rights reserved.

The main use of ASSERT-PV is to compute thermalhydraulic parameters in a horizontal CANDU fuel channel, including pressure drop, critical heat flux (CHF) location, dryout power, and post dryout (PDO) fuel sheath temperature, for steady-state or slow transient flows. With financial support from utilities through CANDU Owners Group, Atomic Energy of Canada Limited (AECL) has developed a new version of ASSERT-PV, v3.2 released in 2012, with significant improvements/enhancements in flow-distribution, CHF and PDO heat transfer models. A series of four papers are devoted to presenting major results of the code-development project. The history of the ASSERT-PV code and the development of ASSERTPV 3.2 flow-distribution, CHF and PDO model sets are described in Rao et al. (2014, Part 1). Code and model assessment for prediction of subchannel flow distributions is presented in Nava-Dominguez et al. (2014, Part 2). The assessment for prediction of dryout power and CHF locations in CANDU bundles is reported in this paper

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Nomenclature Atomic Energy of Canada Limited AECL ASSERT-PV advanced solution of subchannel equations in reactor thermalhydraulics, pressure–velocity solution procedure mean difference AVG BLA boiling length average CHF critical heat flux CANFLEX CANDU FLEXable fuel (43-element bundle) CANDU CANadian Deuterium Uranium LUT look-up table OPG Ontario power generation PT pressure tube post-dryout PDO RMS root-mean-square SL Stern Laboratories standard deviation STD Subscripts CW cold wall effect enh enhancement subchannel size (diameter) size x quality

(Part 3); the assessment for prediction of PDO sheath temperatures is presented in a subsequent paper (Cheng et al., 2014, Part 4). The ASSERT-PV 3.2 development focused on improving code prediction of (i) flow distribution, (ii) dryout power and CHF location, and (iii) PDO sheath temperature distribution. The significant model changes or additions in ASSERT-PV 3.2 (v3.2), compared to the previous version ASSERT-PV V3R1 (the format of the code version identifier has changed during the course of new code development) are described in Rao et al. (2014). For the improvement of the CHF model set, the development focused on incremental improvements to the existing code implementation rather than considering completely new models. The effort was focused mainly on implementing a new CHF look-up table (LUT) and on the development and improvement of CHF correction factor models for the CHF table look-up method. The CHF table look-up method, which is subchannel local condition based, has been the recommended model option in previous code versions due to its wider application range compared to the other CHF correlations or empirical models available in the code. ASSERT-PV 3.2 continues to use this option in developing an improved model set, with additions of the boiling length average (BLA) model, the cold-wall effect model, and improved models for the CHF quality/gap effects and the CHF enhancement effect (by bundle appendages) (Rao et al., 2014). Assessments of the improved capabilities for flow distribution, dryout power and CHF location, and PDO sheath temperature predictions have been completed using experiment data sets including the Stern Laboratories’ 28-, 37- and 43-element bundle experiments. Significant improvement has been confirmed for all key output parameters and over all the three CANDU bundles. Refs. Nava-Dominguez et al. (2014) and Cheng et al. (2014), respectively, present the assessment results for the flow-distribution and PDO calculations, whereas this paper focuses on the assessment of CHF predictions. Since this paper is Part 3 of the four-paper series on ASSERT-PV 3.2, readers who are interested in the details of the code models are advised to read this paper together with Ref. Rao et al. (2014, Part 1). Subsequent sections in the paper are arranged as follows: (i) ASSERT-PV code assessment guidelines and methodology; (ii) SL CHF experiments and ASSERT idealization; (iii) ASSERT-PV results

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and accuracy; (iv) sensitivity study of each model change; and (v) conclusions. 2. Code assessment guidelines and methodology 2.1. Code assessment guidelines The following principles are followed in the current ASSERT code assessment: Data qualification should be examined for the selected datasets, test series, and each selected individual test for code assessment. The following data qualifications should be satisfied: • the experimental parameters were measured and recorded at sufficient accuracy and sampling frequency, and the measurement uncertainties are known or can be estimated, • test boundary and initial conditions to be applied to the ASSERT input model were recorded at sufficient detail and accuracy to allow simulation of the tests, • test facility configuration and geometry are described with sufficient detail and accuracy for the ASSERT input model, • test results are reasonable and self-consistent with all anomalies been explained, problems identified and reported issues resolved, and • experimental data used in the current code assessment are independent of those for developing correlations or models in ASSERT-PV 3.2 and in the previous code versions. The selected experimental data should be close to the ASSERT intended application range. This is to ensure that the ASSERT code is assessed for the qualification of safety analyses under normal operating conditions and various accidental scenarios. The ASSERT intended application range for light water is: • • • • • •

channel outlet pressure: 6–11 MPa channel inlet flow rate: 7–25 kg/s channel power: up to 15% overpower beyond the onset of CHF channel outlet qualities: up to 100% channel inlet temperature: 230–270 ◦ C pressure tube diametric creep: 0–5.1%.

One recommended model set is to be applied to cover all CANDU bundle geometries and operating conditions; i.e., user input would remain the same except for the bundle geometry information. This model set for the code assessment is based on the knowledge and experience accumulated in recent ASSERT code development. No “tuning” of model constants or coefficients is allowed during the assessment so as to increase the degree of confidence and credibility in the assessment (see Section 3.2). This is also to ensure that the ASSERT-PV 3.2 code can be used for the new bundle design in the future. 2.2. Code assessment methodology The ASSERT code accuracy is determined by the quantification of the closeness of the code prediction to the measured value. The prediction error, or residual, is the difference between the prediction and the corresponding experimental (measured) value. The mean value of a set of residuals over a range of a key parameter is calculated to provide an estimate of the code bias applicable over that range. The uncertainty or variability of the code bias is determined statistically based upon observation of the distribution of the residuals about the mean. The standard deviation of the residuals is used to express this variation in the code bias. The mean (AVG) and standard deviation (STD) can be combined into a single

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statistic that reflects both the average difference and the variation in the differences: the root-mean-square (RMS) of the residuals. These statistics (AVG, STD, RMS) are calculated and used to quantify the ASSERT code accuracy for the CHF predictions. They are calculated for a subset of the tests in each exercise (e.g., for a Stern Lab test series representing a single pressure-tube profile), but the overall bias, standard deviation and RMS of the differences between the predicted and measured dryout power are also reported, and based on as many individual tests and measurements as possible. The contributions of the newly developed (or modified) CHF models to the CHF prediction improvement are assessed by the model sensitivity studies. Table 1 shows the comparison of the ASSERT-PV 3.2 CHF model set and the V3R1 model set (Rao et al., 2014). The separate effect of each model change is quantified by comparing the prediction result obtained by using all the recommended v3.2 CHF model changes with that obtained by excluding that particular model change. The overall effect of the CHF model changes is assessed too by excluding all CHF model changes to V3R1, resulting in an ASSERT-PV model set that combines the V3R1 CHF model set with the v3.2 flow-distribution model set. 3. Experiment data and ASSERT idealization The assessment of the recommended CHF model set uses the full-scale SL CHF experiments. 3.1. Stern Lab bundle tests Several experimental programs were conducted at SL to evaluate CHF and thermalhydraulic behaviors of the 28-element (Fortman, 2010), 37-element (Fortman et al., 1997; Fortman, 2011), and CANFLEX (43-element) (Dimmick et al., 1999; Leung et al., 2001) fuel designs. Single- and two-phase tests were performed over a range of thermalhydraulic conditions using one uniform and two non-uniform internal diameter flow channel profiles, which simulate, respectively, an uncrept and two crept pressure tube (PT) profiles of maximum diametral creep of 3.3% and 5.1%. Each simulated fuel string was comprised of electrically heated elements with simulated end plates and appendages to represent the external geometry of a fully aligned string of twelve fuel bundles. The experiments were set up to obtain the onset-of-dryout power, pressure drop, and PDO sheath temperature for fuel bundles with non-uniform power profiles in uncrept and crept flow channels under conditions relevant to CANDU reactors. Figs. 1–3 show the bundle images (left) and ASSERT subchannel modeling (right) for 28-element, 37-element and CANFLEX (43-element) bundles, respectively. The bundle images show the cross-views of the bundles with appendages (end-plates, spacers, buttons and bearing pads). Each fuel element ring in the bundles can be classified as an inner, intermediate or outer ring, as shown in the left figure of Fig. 2. For the 28-element bundle, the inner ring contains elements #1–4, the intermediate ring contains elements #5–12 and the outer ring contains elements #13–28. For the 37-element bundle, the inner ring contains elements #2–7, the intermediate ring contains elements #8–19 and the outer ring contains elements #20–37. For the CANFLEX bundle, the inner ring contains elements #2–8, the intermediate ring contains elements #9–22 and the outer ring contains elements #23–43. The full-scale 28-element bundle simulator was designed and constructed at SL to simulate twelve aligned Pickering fuel bundles (Fig. 1). The outside diameter of each rod was 15.27 mm cold (cold measurements were made at a temperature of 20 ◦ C and a pressure of 103 kPa, with no power or flow). The full-scale 37element bundle was similar to the Bruce and Darlington CANDU Nuclear Generating Station fuel bundles (Fig. 2), each having two

endplates, five planes of bearing pads and one plane of spacer pads. The outside diameter of each rod was 13.06 mm cold. The full-scale 43-element (CANFLEX) bundle simulator was designed and constructed to simulate an Advanced CANDU Reactor (Fig. 3). The length of each simulated fuel bundle was 495.3 mm cold. The overall bundle outer diameter (OD) was 102.5 mm (cold). Two element diameters were utilized in the CANFLEX design. The center and seven inner ring elements had a nominal diameter of 13.5 mm (cold) whereas the 14 intermediate and 21 outer ring elements had a nominal diameter of 11.5 mm (cold). The experiments covered bearing pad heights of 1.4 (Phase 1), 1.7 and 1.8 mm (Phase 2). In SL tests, the experimental fuel string simulated 12 identical, fully aligned bundles (Bundles A–L as shown in Fig. 4), each of which is 495.3 mm long. The experimental fuel string was electrically heated with a nominal heated length of 5.76 m The wall thickness of the elements varied axially to produce a non-uniform, symmetrical axial heat flux distribution (AFD) for 28-element bundles, and a downstream-skewed cosine-shaped AFD for 37-element and CANFLEX bundles, as shown in Fig. 5. The radial heat flux distribution (RFD) increased from the center to the outside of the bundle. The specified inner to outer ring linear to average power ratios were based on design calculations to simulate reactor fuel flux depression for fresh natural uranium fuel. For the RFD of 28-element bundle (Fortman, 2010), the specified ring to average power ratios were 0.78/0.902/1.104 from the inner to the outer ring of elements. The fuel string had a maximum operating power level of 9.5 MW with a design pressure of 11 MPa and a design maximum local sheath temperature of 650 ◦ C. For 37-element bundles (Fortman et al., 1997; Fortman, 2011), the ratios of ring to average heat flux were 0.828/0.860/0.932/1.101 from the center element to the outer ring of elements. The design parameters of the fuel strings were maximum operating power of 12.5 MW at 220 V DC with a design pressure of 13.5 MPa and a maximum local sheath surface temperature of 650 ◦ C. For CANFLEX bundles (Dimmick et al., 1999; Leung et al., 2001), the RFD ratios of ring to average heat flux, were 0.910/0.951/0.902/1.090. Hot dimensions were calculated assuming an inlet coolant temperature of 268 ◦ C, exit pressure of 11 MPa, flow of 18 kg/s and bundle power of 9.0 MW. The design parameters of the fuel strings were maximum operating power of 13.5 MW at 240 V DC, a maximum operating pressure of 11.5 MPa, and a maximum local sheath surface temperature of 600 ◦ C. SL also simulated pressure tube (PT) aging effect during normal reactor operation. Fig. 6 shows the two crept PT profiles of maximum diametric creep of 3.3% and 5.1%. Table 2 lists the SL CHF tests used in the assessment of the ASSERT-PV 3.2 CHF model set, which is recommended to be used with the new v3.2 flow distribution models (Nava-Dominguez et al., 2014). The test conditions are consistent with the ASSERT intended application range. 3.2. ASSERT idealization The ASSERT model for the SL bundle channel is set up based on the test section dimensions and the test conditions from the experiments described in Section 3.1. 3.2.1. Subchannel geometry The SL test section geometry is modeled in ASSERT-PV by a number of discrete control volumes that, taken together, cover the whole channel. The channel is divided into 41 subchannels for 28-element bundle, 60 subchannels for 37-element bundle, and 70 subchannels for CANFLEX bundle. These subchannels are defined as the coolant flow area bounded by the rod surfaces and imaginary lines joining adjacent rod centers. The right pictures in Figs. 1–3 show the subchannel discretization of the SL 28-element,

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Table 1 ASSERT-PV v3.2 CHF model set compared to V3R1. Mod V3R1

Model 3.2

Comments

Flow distribution models

Previous models (V3R1)

v3.2 flow distribution model (Rao et al., 2014; Nava-Dominguez et al., 2014)

The recommended v3.2 flow distribution model set is superior to V3R1 model set (Nava-Dominguez et al., 2014).

CHF look-up table

1995

2005

LUT 2005 (Groeneveld et al., 2005) reduces prediction STD when the “right” flow and CHF correction models are used (Rao et al., 2014).

BLA model

No

BLA model with lower bound

KBLA = qlocal /qBLA , KBLA lower-bounded by 0.8 in expectation of reduced BLA effect in an “open” subchannel with bundle appendages (Rao et al., 2014).

Subchannel size (diameter) correction exponent coefficient n

1/3, but 0 in effect (Rao et al., 2014)

1/2

Ksize = (0.008/Dh ) . Recent CHF look-up tables are associated with n = 1/2 (Rao et al., 2014; Groeneveld et al., 2005).

Cold-wall effect and relaxation factor  CW (0.0–1.5)

N/A

KCW with default,  CW = 1.0

KCW = 1 − CW (1 − 1/2 ), where  = Dh /Dheated . The cold-wall model is similar to others in literature in using Dheated /Dh to correlate the effect.  CW : relaxation factor (Rao et al., 2014).

CHF enhancement by bundle appendages

Existing CHF enh. model (Rao et al., 2014)

Modified CHF enh. model (Rao et al., 2014)

Based on a previous R&D work. The model reduces CHF enhancement effect (Doerffer et al., 2000) by considering an “enlarged” subchannel area including regions of gaps connecting neighboring subchannels (Rao et al., 2014). Model constant  enh is set to 1.0 (default).

Quality effect, relaxation factor:  x

0.25

0.5

Kx = 1 − x (1 − Kx∗ ), Kx∗ is the CHF penalty ratio obtained based on experiment data. Justification of an under-relaxation of the effect was based on the consideration that data used in the original model (Groeneveld et al., 1992) included the cold-wall effect (Rao et al., 2014).

37-element and CANFLEX bundles, respectively, together with the element and subchannel numbering used by ASSERT-PV.

3.2.2. Axial nodalization The length of the channel simulated by ASSERT is 6.439 m for each bundle test. This length is equivalent to the 13-bundle length of the pressure drop measurements described in Refs. Fortman (2010, 2011) and Dimmick et al. (1999). Note that the simulated

n

13-bundle length consists of the 12 heated bundles and approximately half an unheated bundle at each end. The total bundle length (6.439 m) is divided into 156 (12 per bundle) non-uniformly sized axial zones using a user specified axial zone table.

3.2.3. Axial pressure-tube creep profiles The axial variation in pressure-tube diameter is specified in the ASSERT input by a table of axial variation factors. This affects the

Fig. 1. Image of a 28-element bundle and ASSERT subchannel modeling (uncrept PT).

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Fig. 2. Image of a 37-element bundle and ASSERT subchannel modeling (5.1% (max) crept PT).

Fig. 3. Image of a CANFLEX (43-element) bundle and ASSERT subchannel modeling (uncrept PT).

Fig. 4. Test section in Stern Lab tests.

subchannel flow areas, and heated and wetted perimeters, intersubchannel gap widths, and the subchannel centroid-to-centroid distances and associated angles for the outer subchannels next to the flow tube. These subchannel geometries are computed by the geometry pre-processor using the relative pressure tube diameter at each relative axial location (The relative pressure tube diameter is defined as the local crept diameter over the nominal pressure tube diameter as shown in Fig. 6). 3.2.4. Boundary conditions The ASSERT-PV input file provides the information for the experimental axial and radial heat flux distributions (AFD and RFD) to compute the heat flux over each axial zone and each element ring. Other boundary conditions, such as the channel fluid inlet temperature, mass flux (inlet mass flow rate), channel outlet pressure and applied channel average heat flux (input power) are

determined from the reported measurements, and specified for each test case through a series of stacked input records. The enthalpy (temperature) distribution at the inlet is assumed uniform across all subchannels. The mass flow rate at the inlet is split by the ASSERT code to equalize the axial pressure drop in each subchannel at the inlet region. 3.2.5. Fluid properties Light water was used in the SL tests. The ASSERT HLWP package is used to determine the saturated and unsaturated thermodynamic properties of light water and vapour. 3.2.6. Flow distribution modeling The CHF calculations are inevitably involved with flow distribution calculations. The friction factors, multipliers and heat transfer correlations are specified in the input file with the

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Fig. 5. Axial heat flux distribution (AFD).

Fig. 6. Flow channel profiles for Stern Lab tests.

recommended ASSERT flow distribution model set (Rao et al., 2014; Nava-Dominguez et al., 2014). This CHF assessment uses the Colebrook–White single-phase turbulent friction factor (with no heated wall viscosity correction factor) and the Friedel correlation

for the two-phase friction multiplier. The homogeneous two-phase multiplier is used for the form loss calculations. The wall-to-fluid heat transfer model is selected such that the Chen correlation is applied for void fractions up to 20% (the Chen correlation is used

Table 2 Summary of experiment datasets. Bundle

28-E

PT creep or bearing pad

Uncrept (with/without 90◦ bundle rotation) 3.3% creep (90◦ bundle rotation)

37-E 1990s 37-E 2009

CANFLEX (43-E) Phase 1

CANFLEX (43-E) Phase 2

Test series

R1 – 96 cases R2 – 42 cases (90◦ rotation) C1 – 124 cases

Operating conditions Pressure (MPa)

Inlet temperature (◦ C)

Channel flow rate (kg/s)

5–11

225–275

7–24

Uncrept 3.3% creep 3.3% creep 5.1% creep

R2 – 40 cases C1 – 48 cases C4 – 200 cases C3 – 163 cases

6–11

225–280

7–23

Uncrept, BP 1.4 mm 3.3% creep BP 1.4 mm 5.1% creep BP 1.4 mm Uncrept, BP 1.8 mm 5.1% creep, BP 1.8 mm 5.1% creep, BP 1.7 mm 3.3% creep, BP 1.7 mm Uncrept, BP 1.7 mm

R1 – 48 cases C2 – 63 cases C1 – 70 cases B1 – 84 cases B2 – 49 cases B3 – 45 cases B4 – 50 cases B5 – 75 cases

6–11

200–290

10–29

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Fig. 7. Comparison of ASSERT-PV 3.2 and V3R1 for dryout power prediction.

for the liquid convective and nucleate boiling heat-transfer coefficient, and the Ahmad correlation for higher void fractions, Rao et al., 2014. For single-phase flow, the Chen correlation reverts to the Dittus–Boelter correlation). The subchannel mixing models and parameters are the modified Carlucci thermal and momentum mixing and void diffusion mixing model, Rowe’s equilibrium void model, Rehme’s correlation for thermal and momentum mixing of subchannel pairs (Rao et al., 2014; Nava-Dominguez et al., 2014). Default incremental void mixing multiplier and thermal and momentum mixing obstruction factors are used in the code assessment (Rao et al., 2014; NavaDominguez et al., 2014). 3.2.7. CHF modeling The v3.2 recommended CHF model set used in the current CHF assessment is briefly described below, with details being referred to Rao et al. (2014). • CHF LUT 2005 is used instead of the previous version CHF LUT 1995. The new LUT resolved a prediction accuracy issue of the old LUT in the so-called “Limiting Quality Region (LQR)” (Groeneveld et al., 2005) characterized by a fast decrease of CHF with an increase in steam quality. The new LUT has an enhanced quality of database leading to better predictions of CHF. • The subchannel-size correction model is activated and the exponent coefficient is set to 1/2 for consistency with the use of CHF LUT 2005. This correction factor often has significant effect on predicted dryout power and CHF location since there are many subchannels with hydraulic diameters significantly different from 8 mm, which is used for generating the CHF look-up-table 2005. • The modification to the CHF enhancement correction factor reduces the CHF enhancement effect by considering an “enlarged” subchannel area (for calculation of this factor only) that includes regions of gaps connecting neighboring subchannels. • The BLA correction model is chosen as the recommended option against the local-condition CHF approach, and a lower bound of 0.8 (or 80%) is imposed to limit its effect because CANDU bundle appendages are expected to make upstream flow history less relevant compared to a tube geometry without these appendages, again because of the presence of adjacent subchannels. • The new cold-wall effect correction factor in ASSERT-PV 3.2 accounts for the CHF penalty effect due to existence of a cold (or unheated or adiabatic) wall or rod segment that causes increased imbalance in flow and enthalpy distribution within a subchannel. In most CANDU applications, the relevant

subchannels are the outer subchannels adjacent to the unheated pressure tube. • The quality/gap effect (gap-correction) model is revised with the relaxation coefficient changed from a previous value of 0.25 (75% discount of the effect compared to that in a heated annular channel) to 0.5 (50% discount). 3.2.8. Calculation control The calculation control options are specified in the input file. The maximum numbers of energy (enthalpy) iterations, inner (mass) iterations, outer (flow) iterations, are set conservatively to 20, 20 and 150, respectively. The relative residual change criteria for enthalpy, flow, mass equation, lateral and axial momentum are set to 10−6 , 10−4 , 10−6 , 10−3 and 10−3 , respectively. Note that the test cases are executed using the stacked runs and these numbers of iterations ensures good convergence for all the test cases stacked in a single input file (for a certain test series). 4. ASSERT-PV results and accuracy The current assessment is made by the comparison of the prediction accuracy of dryout power, using the prediction statistics including the mean difference (AVG), the standard deviation of the differences (STD), and the root-mean-square difference (RMS) in dryout power. Improvement of CHF location prediction is one of the model development targets and the assessment also includes the comparison of the prediction accuracy of CHF axial and radial locations. In comparing radial CHF location, emphasis is placed on accurately predicting both the element ring and the subchannel ring, i.e., CHF at the correct element ring facing the correct side (facing inside toward bundle center or facing outside toward the PT, rather than on individual elements or subchannels. Table 3 lists the statistics of assessment of the ASSERT-PV 3.2 model set (herein referred to as Model 3.2) against the ASSERT V3R1 model set (V3R1) for the predication of dryout power. The related v3.2 code bias is −0.4% (AVG) for 28-element bundles, −2.5% for 37-element 1990s tests, −3.1% for 37-element 2009 tests, −2.3% for CANFLEX Phase 1 tests and −0.7% for CANFLEX Phase 2 tests. The overall code bias is −1.1% for all three bundle types. The assessment confirms that the v3.2 code bias is significantly smaller than the V3R1 code bias. The RMS differences obtained from Model 3.2 are also smaller than those from the ASSERT V3R1 model set, indicating that Model 3.2 is superior to the previous model set for the dryout power predictions. The most significant improvement in dryout power can be identified for the 28-element and CANFLEX bundle tests, as shown in

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Table 3 Prediction statistics: dryout power. Bundle

PT creep (%)

Statistics

V3R1 (%)

Model 3.2 (%)

28e (262 cases)

0,3.3

AVG STD RMS

10.6 5.8 12.1

−0.4 3.7 3.7

37e-1990s (88 cases)

0,3.3

AVG STD RMS

−5.3 4.5 7.0

−2.5 5.7 6.2

37e-2009 (363 cases)

3.3,5.1

AVG STD RMS

−6.9 6.7 9.6

−3.1 8.7 9.2

43e-Phase 1 (181 cases)

0,3.3,5.1

AVG STD RMS

9.1 5.2 10.5

2.3 4.2 4.8

43e-Phase 2 (303 cases)

0,3.3,5.1

AVG STD RMS

6.6 6.4 9.2

−0.7 4.5 4.5

All (1197 cases)

0,3.3,5.1

AVG STD RMS

2.9 9.7 10.1

−1.1 6.3 6.4

Fig. 7. In the 28-element and CANFLEX bundle tests, most CHF occurred on the outer ring, where the heat transfer is significantly affected by the cold wall of the pressure tube. The newly developed and modified CHF models significantly reduce the dryout power prediction errors for these tests. The current assessment shows that the V3R1 and v3.2 CHF model sets predict the axial location of CHF similarly well, but v3.2 predicts the radial location significantly better. Figs. 8–12 show the prediction statistics of CHF radial locations for each bundle test. Unlike the CHF axial location predictions, the V3R1 CHF model set fails in the CHF radial location predictions for the 28-element and CANFLEX bundle tests. However, Model 3.2 accurately predicts the CHF radial locations for most test cases regardless of their bundle types. For 28-element tests, Model 3.2 accurately predicts the number of cases of CHF at outer-ring elements facing outside (toward PT), which accounts for 87% of the test points (Fig. 8). For 37element tests, Model 3.2 accurately predicts most cases of CHF at an inner-ring element (Figs. 9 and 10), whereas for CANFLEX tests, Model 3.2 accurately predicts most cases of CHF at an outer-ring element (Figs. 11 and 12). Model 3.2 is assessed to be superior to

Fig. 8. Prediction of CHF radial locations for 28-E tests.

the V3R1 model set in the prediction of CHF radial locations. This capability is important in applications for bundle geometry optimization or for bearing pad height design. 5. Model sensitivity studies Sensitivity studies are performed to quantify the contribution of each CHF model change and the overall effect of the CHF model changes to the improvement in dryout power and CHF location predictions. Following the code assessment methodology (Section 2), the effect of each model change is assessed using the recommended v3.2 CHF model set but excluding that particular model change. Similarly, the overall effect of the CHF model changes can be assessed by excluding all CHF model changes to V3R1, resulting in an ASSERT-PV model set that combines the V3R1 CHF model set with the v3.2 flow-distribution model set. 5.1. Dryout power prediction Table 4 lists prediction statistics of dryout power for each sensitivity-study case, designed to assess the effect of a particular model change. The expectation is that each and every

Fig. 9. Prediction of radial CHF locations for 37-E 1990s tests.

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Table 4 Sensitivity study: summary of prediction statistics of dryout power. V3R1 CHF enhancement (%)

V3R1 quality effect  x = 0.25 (%)

All CHF model changes, not used (%)

5.0 3.6 6.2

4.8 3.8 6.1

11.7 4.8 12.6

−5.0 6.8 8.5

−2.5 5.7 6.2

1.2 6.2 6.3

2.7 7.3 7.8

−2.9 8.7 9.2

−4.5 9.9 10.9

−3.1 8.7 9.3

0.5 9.8 9.8

2.8 10.7 11.0

6.5 4.2 7.8

4.5 4.3 6.3

2.8 4.1 5.0

2.3 4.2 4.8

6.9 4.0 8.0

12.4 4.4 13.2

−1.1 5.0 5.1

3.8 4.3 5.7

2.4 4.1 4.8

0.4 4.5 4.6

−0.7 4.5 4.5

4.6 4.1 6.2

10.6 5.1 11.7

−1.1 6.6 6.7

3.0 6.8 7.4

0.2 6.6 6.6

−0.8 7.3 7.4

0.1 6.8 6.8

3.5 6.9 7.7

8.2 8.4 11.7

Bundle

Statistics

Model 3.2 (%)

LUT 1995 (%)

No BLA model (%)

No sub-channel size correction (%)

28-e

AVG STD RMS

−0.4 3.7 3.7

0.0 4.0 4.0

4.2 3.6 5.6

−0.1 3.7 3.7

1.9 4.1 4.5

37-e 1990s

AVG STD RMS

−2.5 5.7 6.2

−2.7 6.3 6.8

0.9 6.1 6.2

−2.2 5.6 6.0

37-e 2009

AVG STD RMS

−3.1 8.7 9.2

−3.0 9.1 9.6

0.1 9.6 9.6

43-e Phase 1

AVG STD RMS

2.3 4.2 4.8

1.9 4.3 4.7

43-e Phase 2

AVG STD RMS

−0.7 4.5 4.5

Overall

AVG STD RMS

−1.1 6.3 6.4

No cold-wall effect  CW = 0.0 (%)

sensitivity case should show an increase in RMS difference compared to the base (v3.2) case, confirming a positive effect on CHF prediction accuracy. For 28-element bundle tests, dryout power prediction is found to be improved significantly by the modified cold-wall effect model; a RMS reduction of 2.5% in dryout power, from the 6.2% obtained by excluding the cold-wall effect to the 3.7% by the recommended v3.2 model set, as shown in Table 4. The combined effect of all CHF model changes is a RMS reduction of 8.9%, from the 12.6% obtained by no CHF model changes (i.e., the V3R1 CHF model set) to the 3.7% by the v3.2 CHF model set. The sensitivity study also shows that the modified BLA model and quality/gap effect model are superior to their V3R1 counterparts in dryout power prediction. The RMS is 4.3% using the V3R1 BLA model, and 6.1% using the V3R1 quality effect correction model, respectively, as compared to 3.7% by the v3.2 CHF model set. For 37-element tests, the prediction is significantly improved by the subchannel-size correction model, but the effects of other model changes are insignificant. For the 37-elemnet 1990s tests, the combined effect of all model changes is a RMS reduction of 1.6%, from the 7.8% obtained by no CHF model changes to the 6.2% by the

v3.2 CHF model set. For the 37-elemnet 2009 tests, the combined effect of all CHF model changes is a RMS reduction of 2.8%, from the 11.0% by no CHF model changes to the 9.2% by the v3.2 CHF model set. For CANFLEX tests, all the CHF model changes improve the prediction of dryout power except for the cold-wall effect model. The dryout power prediction is significantly improved by the BLA model (by 3.0% in RMS) and the gap/quality effect model (by 3.2%) for the CANFLEX Phase 1 tests. Similar effects of the two model changes can be observed also for the Phase 2 tests, but with a smaller degree of improvement. The combined effect of all CHF model changes is a reduction in RMS of 9.6%, from the 13.2% by no CHF model changes to the 4.8% by the v3.2 CHF model set for the Phase 1 tests, and a RMS reduction of 7.2%, from 11.7% to 4.5%, for the Phase 2 tests.

Fig. 10. Prediction of CHF radial locations for 37-E 2009 tests.

Fig. 11. Prediction of CHF radial locations for 43-E Phase 1 tests.

5.2. CHF axial location prediction Due to the fact that the V3R1 model is also capable of predicting the CHF axial location, the statistics of sensitivity of predicted CHF axial location to each model change is not tabulated in this paper, but the sensitivity results are still briefly reported here.

Table 5 Sensitivity study: summary of prediction statistics of CHF radial location. Bundle

Rod ring

28-e

Interm. Outer Inner

37-e 1990s

Interm. Outer Inner

37-e 2009

Interm. Outer Inner

43-e Phase 1

Interm. Outer Inner

43-e Phase 2

Interm. Outer

Inside Outside Inside Outside Inside Outside

Stern

6 6 24 226

Model 3.2

LUT 1995

No BLA

Existing CHF enh. model

No subch. No size correc. cold-wall model effect,  CW = 0

Existing quality effect,  x = 0.25

Existing BLA

No CHF enhancement

Subch. size corr. expon. (n = 1/3)

Cold-wall effect,  CW = 1.5

No quality effect,  x = 0.0

15

18

17

17

17

20

15

18

12

17

16

16

23 224

33 211

34 211

27 218

186 59

199 43

37 210

24 220

64 186

31 214

19 227

36 210

Inside Outside Inside Outside Inside Outside

54 7 22

65

65

65

65

69

65

65

66

12

66

64

65

11

14

14

11

7

11

16

14

49

10

11

21

5

12

9

9

12

12

12

7

8

27

12

12 1

2

Inside Outside Inside Outside Inside Outside

138 114 100 4 5 2

191

186

186

192

206

191

186

198

11

193

191

186

139

155

161

140

128

139

162

157

250

138

139

169

33

22

16

31

29

33

15

8

102

32

33

8

4 7

3 12

5 12

5 12

5 33

4 10

8 8

7 4

1

4 15

4 6

12 11

167 3

158 8

164

135 29

143

167

162 3

152 18

178 2

162

125 46

158

33

3 35

2 42

57

2 101

33

41

3 33

57

33

270

265

259

246

200

270

262

267

246

269 1

Inside Outside Inside Outside Inside Outside Inside Outside Inside Outside Inside Outside

1

109 71

267 36

303

Y.F. Rao et al. / Nuclear Engineering and Design 276 (2014) 216–227

Inner

Inside/ outside

5 49

249

225

226

Y.F. Rao et al. / Nuclear Engineering and Design 276 (2014) 216–227

which CHF occurs at the outer-element rings facing outside toward the PT for most of the cases, but it has no effect on the prediction of 37-element and CANFLEX bundles. The modified CHF enhancement model improves significantly the prediction of dryout power for CANFLEX Phase 1 tests, but it has no significant effect for 28element and 37-element bundle tests when compared with the existing CHF enhancement model. The gap/quality effect model was found to improve significantly the predictions of dryout power for 28-element and CANFLEX tests, and of axial CHF location for CANFLEX tests. The BLA model improves significantly the prediction of dryout power for 28-element and CANFLEX tests. It also improves the axial CHF location prediction, except for the 28-element bundle tests.

6. Conclusions Fig. 12. Prediction of CHF radial locations for 43-E Phase 2 tests.

The CHF axial location prediction is slightly improved by the CHF LUT 2005, the modified CHF enhancement model and the modified quality effect model for 28-element bundle tests. For 37-element tests, the CHF axial location prediction is improved by all the model changes except for the cold-wall effect model, which has no effect if no CHF is predicted at the outer-ring facing outside toward the pressure tube. For CANFLEX tests, the CHF axial location prediction is significantly improved by the modified quality effect model and BLA model. Similar to 37-element tests, the cold-wall model has no effect on the improvement of CANFLEX CHF axial location prediction. 5.3. CHF radial location prediction Significant improvement in radial CHF location prediction is one of the major features of the v3.2 model set. Table 5 summarizes the predicted radial CHF locations compared to the Stern Lab experiments, in the form of the number of cases of CHF initiation at certain element rings and facing certain direction (inside or outside). For 28-element bundle tests, the radial location prediction is improved by all the CHF model changes, but the subchannel-size correction model and the cold-wall effect model contribute the most improvement. Without these two model changes, CHF would be predicted at the outer-ring facing “inside”, rather than facing “outside” as measured in the experiment, for most of the cases (see Table 5). This confirms that neither the subchannel-size effect nor the pressure-tube cold-wall effect can be ignored in accurate prediction of CHF radial location. For 37-element tests, the CHF radial location prediction is relatively insensitive to most model changes. For CANFLEX bundle tests, the CHF radial location prediction is significantly improved by the subchannel-size correction model. The other model changes are found to have minor (mixed) effects on the prediction of CHF radial location. 5.4. Summary of sensitivity studies The CHF LUT 2005 was found to be superior to the 1995 LUT in reducing the code bias and associated standard deviation, but the new look-up table does not improve significantly the prediction of CHF location. The subchannel-size (diameter) correction model improves significantly the prediction of dryout power and axial CHF location for 37-element bundles. It also improves the prediction of radial CHF location for 28-element and CANFLEX tests. The coldwall effect model was found to improve significantly the prediction of dryout power and CHF location for 28-element bundle tests, in

This paper presents an assessment of the subchannel code ASSERT-PV 3.2 for prediction of dryout power and CHF location in CANDU bundles. Code predictions were compared with measurements from Stern Laboratories’ full-scale 28-element, 37-element and CANFLEX bundle tests conducted in 1990s and in 2009, which encompass the bundle geometries and range of flow conditions for the intended ASSERT-PV applications for existing CANDU reactors. The prediction statistics using the recommended model set of ASSERT-PV 3.2 were compared with those from the previous code version V3R1. Overall, the assessment demonstrated significant improvement in prediction of channel dryout power and axial and radial CHF locations in horizontal fuel channels containing CANDU bundles. Separate-effects sensitivity studies were performed for each CHF model change or enhancement, including the new CHF look-up table and a number of newly developed or modified CHF correction models accounting for the effects of various subchannel geometries and flow conditions that are different from those in a vertical, uniformly heated tube of 8 mm inner diameter. It was demonstrated that overall the CHF model changes reduce the ASSERT code bias, associated standard deviation and RMS difference in prediction of dryout power, and improve significantly the prediction of CHF radial location as well. The ASSERT-PV 3.2 CHF model set is expected to do well for other applications involving small change in bundle geometries or flow conditions, such as applications for OPG’s modified 37element bundles where the bundle geometry change is small and the test conditions are within the ASSERT intended application range. However, it cannot be expected to do similarly well for other applications with flow conditions far beyond the ASSERT application ranges, such as under significantly lower pressures or mass fluxes.

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